Bezier Curves

Bezier curves are smooth curves that are frequently linked together to create paths in computer graphics. It is possible to create degree $n$ curves, but quadratic and cubic are the most common. A Bezier curve between points $A$ and $B$ with degree $n$ will have $n-1$ control points $C_0, C_1, C_2, \ldots$ between $A$ and $B$. A quadratic Bezier curve from $A$ to $B$ is traced by the function $$P(t) = (1-t^2)A+2(1-t)tC_0+t^2B$$ as $t$ ranges from 0 to 1. Similarly, a cubic Bezier curve from $A$ to $B$ is traced by the function $$P(t) = (1-t)^3A+3(1-t)^2tC_0++3(1-t)^2tC_1 + t^3B$$